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Bookmark or Share- What is infinity divided by infinity? - Mathematics Stack ExchangeOne advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator and denominator: infinitesimal, infinite, or appreciable finite, before discussing the technical notion of limit which tends to be confusing to beginners.
- probability - Infinite expected value of a random variable ...From a construction point of view, it is easier to understand. In this particular case, the probability of each outcome decreases exponentially. Since the number of outcomes is infinite, the payout scheme only has to grow at the same rate as the probability of the outcome decreases in order for the series to diverge.
- Uncountable vs Countable Infinity - Mathematics Stack ExchangeAs far as I understand, the list of all natural numbers is countably infinite and the list of reals between 0 and 1 is uncountably infinite. Cantor's diagonal proof shows how even a theoretically complete list of reals between 0 and 1 would not contain some numbers. My friend understood the concept, but disagreed with the conclusion.
- What is the difference between "infinite" and "transfinite"?The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals somehow, which may be giving the wrong impression. But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes ...
- elementary set theory - What do finite, infinite, countable, not ...Clearly every finite set is countable, but also some infinite sets are countable. Note that some places define countable as infinite and the above definition. In such cases we say that finite sets are "at most countable".
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